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Visible Singularities Guided Correlation Network for Limited-Angle CT Reconstruction

Yiyang Wen, Liu Shi, Zekun Zhou, WenZhe Shan, Qiegen Liu

TL;DR

This work addresses the challenge of reconstructing medical images from limited-angle CT data by leveraging visible singularities (VS) and invisible singularities (IVS) theory. It introduces VSGC, a two-stage architecture consisting of a VS-focused edge extractor (VSWD) and a cross-region correlation module (MCA) that uses a sparse, top-k self-attention mechanism, together with a multi-scale anisotropic loss to preserve VS while recovering IVS details. The approach demonstrates superior performance over several baselines on simulated and real datasets, particularly at small angular ranges, achieving notable improvements in PSNR and SSIM, and enabling high-resolution LACT with efficient computation. The work offers a practically impactful direction for LACT reconstruction by aligning network design with the intrinsic directional artifacts and information loss characteristics of limited-angle data, with publicly available code to facilitate adoption and further research.

Abstract

Limited-angle computed tomography (LACT) offers the advantages of reduced radiation dose and shortened scanning time. Traditional reconstruction algorithms exhibit various inherent limitations in LACT. Currently, most deep learning-based LACT reconstruction methods focus on multi-domain fusion or the introduction of generic priors, failing to fully align with the core imaging characteristics of LACT-such as the directionality of artifacts and directional loss of structural information, which are caused by the absence of projection angles in certain directions. Inspired by the theory of visible and invisible singularities, taking into account the aforementioned core imaging characteristics of LACT, we propose a Visible Singularities Guided Correlation network for LACT reconstruction (VSGC). The design philosophy of VSGC consists of two core steps: First, extract VS edge features from LACT images and focus the model's attention on these VS. Second, establish correlations between the VS edge features and other regions of the image. Additionally, a multi-scale loss function with anisotropic constraint is employed to constrain the model to converge in multiple aspects. Finally, qualitative and quantitative validations are conducted on both simulated and real datasets to verify the effectiveness and feasibility of the proposed design. Particularly, in comparison with alternative methods, VSGC delivers more prominent performance in small angular ranges, with the PSNR improvement of 2.45 dB and the SSIM enhancement of 1.5\%. The code is publicly available at https://github.com/yqx7150/VSGC.

Visible Singularities Guided Correlation Network for Limited-Angle CT Reconstruction

TL;DR

This work addresses the challenge of reconstructing medical images from limited-angle CT data by leveraging visible singularities (VS) and invisible singularities (IVS) theory. It introduces VSGC, a two-stage architecture consisting of a VS-focused edge extractor (VSWD) and a cross-region correlation module (MCA) that uses a sparse, top-k self-attention mechanism, together with a multi-scale anisotropic loss to preserve VS while recovering IVS details. The approach demonstrates superior performance over several baselines on simulated and real datasets, particularly at small angular ranges, achieving notable improvements in PSNR and SSIM, and enabling high-resolution LACT with efficient computation. The work offers a practically impactful direction for LACT reconstruction by aligning network design with the intrinsic directional artifacts and information loss characteristics of limited-angle data, with publicly available code to facilitate adoption and further research.

Abstract

Limited-angle computed tomography (LACT) offers the advantages of reduced radiation dose and shortened scanning time. Traditional reconstruction algorithms exhibit various inherent limitations in LACT. Currently, most deep learning-based LACT reconstruction methods focus on multi-domain fusion or the introduction of generic priors, failing to fully align with the core imaging characteristics of LACT-such as the directionality of artifacts and directional loss of structural information, which are caused by the absence of projection angles in certain directions. Inspired by the theory of visible and invisible singularities, taking into account the aforementioned core imaging characteristics of LACT, we propose a Visible Singularities Guided Correlation network for LACT reconstruction (VSGC). The design philosophy of VSGC consists of two core steps: First, extract VS edge features from LACT images and focus the model's attention on these VS. Second, establish correlations between the VS edge features and other regions of the image. Additionally, a multi-scale loss function with anisotropic constraint is employed to constrain the model to converge in multiple aspects. Finally, qualitative and quantitative validations are conducted on both simulated and real datasets to verify the effectiveness and feasibility of the proposed design. Particularly, in comparison with alternative methods, VSGC delivers more prominent performance in small angular ranges, with the PSNR improvement of 2.45 dB and the SSIM enhancement of 1.5\%. The code is publicly available at https://github.com/yqx7150/VSGC.
Paper Structure (25 sections, 1 theorem, 20 equations, 12 figures, 5 tables)

This paper contains 25 sections, 1 theorem, 20 equations, 12 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. LACT Reconstruction
  4. Artifacts and Visible Singularities in Limited Data
  5. Method
  6. Motivation
  7. Network Architecture of VSGC
  8. Visible Singularities Wavelet Dense
  9. Multi-scale Visible Singularity-CrossRegion Correlation Self-Attention
  10. Multi-Scale Loss Function with Anisotropic Constraints
  11. Experiments
  12. Data Specification
  13. AAPM Challenge Data
  14. Periapical Data
  15. Mouse Data
  16. ...and 10 more sections

Key Result

Lemma III.1

quinto2017artifacts Microlocal Regularity Theorem for $\mathcal{L}_\alpha$. where $f$ is a function with compact support, and $\mathrm{WF}(\cdot)$ denotes the wave front set.

Figures (12)

  • Figure 1: LACT boundary reconstructibility correlate with parallelism between boundary tangent directions and X-ray propagation directions. If the tangent line of a body feature's boundary is parallel to a particular scan ray, that boundary will be easily reconstructed. If the tangent line of a body feature's boundary is not parallel to any scan ray, that boundary will be difficult to reconstructquinto1993singularities.
  • Figure 2: Theoretical foundations and design rationale of VSGC: microlocal regularity, wavefront set interpretation. (a) Diagram of microlocal regularity theorem for $\mathcal{L}_\alpha$. (b) The boundary between 1 and 2 is assumed to be the boundary of the tissues within the body, and the boundary between 0 and 1 is assumed to be the boundary between the body and the air. This diagram explains what $WF(\cdot)$ is. (c) The design rationale of our model.
  • Figure 3: Overall design framework of VSGC. VSGC consists of VSWD and UMCA. The design goal of VSWD is to complete the extraction and focusing of VS edge features. Figure a shows the model attention heatmap output by VSWD, which focuses on VS edge features. The design goal of UMCA is to establish the connection between VS edge features and other regions of $\mathcal{L}_\alpha f$, and fully utilize VS edge features to recover the structural information of other regions. Figure b shows the model attention heatmap output by UMCA, which recovers the structural information of other regions while preserving the integrity of VS.
  • Figure 4: VSGC core module architectures. (a) The architecture of VSWD. (b) The architecture of UMCA. (c) The architecture of MCA.
  • Figure 5: WTConv workflow and attention heatmap comparisons. (a) The execution workflow of WTConv. (b) The attention heatmaps of the Dense huang2017densely and the VSWD. VSWD focuses its attention on VS. (c) The attention heatmaps when a baseline attentionvaswani2017attention or UMCA is connected after the same VSWD pre-network. The structural detail level of $i_2$ is higher than that of $i_1$, and MCA achieves better restoration of the IVS, demonstrating its establishment of sufficient and reasonable correlations.
  • ...and 7 more figures

Theorems & Definitions (2)

  • Definition 1
  • Lemma III.1